Lithium battery state of charge – overall introduction and estimation method

What is lithium battery state of charge？

Lithium battery state of charge refers to the state of the remaining power of the battery, that is, how much power is left in the battery. For example, the battery capacity of the Tesla Model 3 is about 60kWh. If it has traveled 200km after being fully charged and there is 40kWh left, then 40kWh is the state of charge of the battery.

But the more common way is to read the remaining power of the battery in the form of a percentage, so for convenience, the SOC of the battery is usually expressed as follows: SOC = Qc/Qn*100%

In this formula, Qc refers to the remaining available power of the battery at a certain moment, and Qn refers to the rated capacity of the battery. So if you want to get the value of SOC, you only need to know the two parameters Qc and Qn. Qn will decrease as the battery ages, but its rate of change is small, so in the final analysis, calculating SOC is calculating Qc.

Why should estimation accuracy of SOC be improved

One of the most important reasons for determining the value of lithium battery state of charge is to allow users to have a clear idea. Taking EV battery cell as an example, if the user knows that the cruising range is about 500km when fully charged, and there is still 50km away from the nearest charging pile, then the user knows that when the remaining power is still 10% to 15%, the user must go to charge or swap station, or to be safer, go to charge when the lithium battery state of charge is 20%.

However, this is not the only purpose of SOC, so the current research needs to find various ways to improve the estimation accuracy of SOC. Assuming that the SOC estimation error is greater than 10%, it means that when the vehicle dashboard displays an SOC value of 20%, the actual SOC may be less than 10%. If the driver continue to drive at this time, it may cause battery over discharge. Overcharging may also occur during charging, and frequent overcharging and overdischarging have a great impact on battery life and lithium battery safety.

What happens when the SOC estimate error is greater than 5%? Perhaps from the perspective of users and battery usage conditions, 5% error is barely acceptable, and many battery manufacturers will mention in the agreement that the SOC estimation accuracy of BMS is less than 5%, so does it mean that 5% error is enough, do not need to continue to improve it? The answer is no.

Battery management is basically carried out around the state of the battery, it is actually to understand the state of the battery, and find a way to make the battery work in the optimal state. In addition to SOC, the state of the battery also includes state of health (SOH), state of power (SOP), state of energy (SOE), etc., so sometimes the battery state is collectively referred to as SOX, but in actual use, we are more concerned about SOC and SOH.

So what about SOH? SOH refers to the health status of the battery and can be used to judge the battery life. The definition of SOH is not uniform, one of the calculation methods is: SOH = Qaged/Qnew. where Qaged is the maximum battery power currently available, and Qnew is the maximum battery power when the battery is not used.

This method is based on the ratio of the current actual capacity of the battery to the rated capacity to define the SOH, for example, when the actual capacity of the battery is reduced to 80% of the rated capacity, it is generally believed that the battery has reached the service life.

This definition method needs to know the exact value of the current capacity, which can generally be charged by the battery at a certain lithium battery state of charge value, and the actual capacity of the battery can be calculated according to the amount of electricity that can be charged when the battery is full.

Therefore, the accuracy of SOH obtained by this method is strictly dependent on the accuracy of SOC. In addition, the realization of functions such as SOP state calculation and power balance of the battery management system need to be based on the value of SOC. It can be said that if the estimation accuracy of SOC is improved, and the overall performance of the battery management system can be optimized and improved, so we need to find ways to improve the estimation accuracy of SOC.

How to estimate lithium battery state of charge

In order to improve the accuracy of lithium battery state of charge estimation, the industry has made a lot of efforts and put forward a lot of methods. According to different principles, these methods can be roughly divided into the following two categories:

Traditional methods

(1) Open circuit voltage method

The open circuit voltage method is to determine the lithium battery state of charge value according to the open circuit voltage OCV of the battery. Taking lithium-ion monomer cells as an example, the voltage can generally reach about 4.2V when fully charged, and the cut-off voltage is about 2.6V when fully discharged. During the charging and discharging process of the battery, the voltage of the battery is constantly changing.

In simple terms, the open circuit voltage of the battery under different SOC values is measured respectively, and then the function about SOC-OCV is obtained by data fitting method.

Then the most critical thing is how to obtain the experimental data, that is, the OCV value of the battery at different SOC values. The impact of the polarization effect of lithium-ion batteries is that the voltage of the battery is not constant for a period of time after the battery stops charging and discharging, but changes slowly. Yes, the voltage obtained after standing for about 1 to 2 hours is the real open circuit voltage under the current lithium battery state of charge.

Therefore, when measuring the relationship between battery SOC and OCV, it is often through HPPC test, that is, Hybird Pulse Power Characterization test. The general process is to discharge 10%, leave it for 1 hour, and cycle back and forth until it is completely discharged.

Another notable feature of lithium-ion batteries is that their characteristics are particularly susceptible to ambient temperature. The favorite temperature range of lithium-ion batteries is about -20°C to 50°C (similar to the temperature range that humans can adapt to), and at different temperatures, its discharge capacity, open circuit voltage, internal resistance and other parameters are not the same , the figure below shows the relationship between SOC and OCV of a cell at different temperatures.

In the HPPC test, the open circuit voltage of the battery is measured after standing for 1 hour. It is obviously unrealistic in actual use. It is impossible for us to stop the electric car and stand still for a period of time just to read the remaining power. Therefore, from this aspect, it is not feasible to estimate the SOC value of the battery through the open circuit voltage, but it can be used to calibrate the inaccurate lithium battery state of charge estimation value.

(2) Ampere-hour integral method

Ampere is the charge and discharge current of the battery and hour refers to the time, and the ampere-hour integration is to integrate the current charged into or out of the battery with the time, and according to the lithium battery state of charge value at the initial moment of the battery, the remaining power in the battery at a certain moment can be obtained.

The principle is roughly expressed by the formula:

When charging: SOC=∫idt/Qn
When discharging: SOC=1-∫idt/Qn

The ampere-hour integration method is easy to operate and has a small amount of calculation, so it has become the most commonly used lithium battery state of charge estimation method. However, the biggest problem with this method is that the SOC estimation accuracy is strictly dependent on the accuracy of the current sensor. If the measured value of the current is inaccurate, the error will accumulate during the integration process, resulting in an increasing error in the final SOC estimation, which seriously deviates from the true value.

When the cumulative error of the battery SOC is too large, we can use the gap when the battery does not work (such as when the electric car is parked at night) as the resting time. Since the battery has been left standing for a long enough time, when the next time the vehicle is started, the open circuit voltage method is used to correct the SOC value of the battery.

Model-based method

In fact, the battery itself is a system in which chemical reactions occur continuously inside, so as to realize charging or discharging through the flow of ions, but this system is relatively complicated, and the intensity and speed of chemical reactions are also affected by many factors, such as temperature and battery life. Therefore, in order to better understand the battery, we can analyze it from its working mechanism, and the most intuitive way is modeling.

The first type of model is the electrochemical model. This type of model is based on the porous electrode theory and the concentrated solution theory. The charge-discharge behavior of lithium-ion batteries is described at the mechanistic level. Commonly used electrochemical models include quasi-two-dimensional models and single-particle models.

The principle of the electrochemical model is similar to the white box model in machine learning. Although this model tries to analyze the problem from the working mechanism, the biggest problem is that the calculation is too large and the online application ability is poor.

The second type of model is the equivalent physical model. Since the battery can provide voltage externally, a voltage source is placed in the physical model; since the battery is resistive inside, a resistor is placed; this is the principle of the internal resistance model Rint.

Once the battery model is determined, the next step is to determine the model parameters of the battery. Taking the Thevenin model as an example, a parameter identification method is required to determine the values of resistance, capacitance, and inductance in the model. The methods of parameter identification can also be divided into two categories: offline and online.

The off-line parameter identification method is to determine the model parameter value of the battery from the battery data obtained through the battery charge and discharge test before the battery is used, and then estimate the lithium battery state of charge assuming that the value remains unchanged. However, the ambient temperature of the battery is different and the number of cycles of use is different, so the model parameter values must change. Therefore, although the offline parameter identification method is simple, there will be errors.

The other type is the online method, where online refers to continuously correcting the model parameters of the battery during the life cycle of the battery, thereby improving the accuracy of the model. But the disadvantage is that it is too complicated, so it is not convenient for practical application.

There are many model-based SOC estimation methods, such as Kalman filter and its improvements (EKF, UKF, etc.), particle filter, etc. In fact, if these methods are doing one thing, it is to find the optimal state value of the battery from the data full of errors. Errors are everywhere, and we have no way to completely eliminate errors, but we can use statistical ideas (such as Bayesian estimation, maximum likelihood estimation, etc.) to find out the rules from these chaotic data and obtain the optimal solution.

The biggest feature of the model-based SOC estimation method is that it can minimize the estimation error caused by measurement noise, but the practicability of these methods is still very limited. On the one hand, the battery is not as obedient as we imagined.

There are too many factors that affect the state of the battery during use, and it is difficult to fully express the model. Core, BMS will collect a lot of data, and the processing of these data itself has a relatively heavy workload, so many optimization algorithms are limited by computing power and cannot exert their value at all.